{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "initial-change",
   "metadata": {},
   "source": [
    "<h1> <big> <center> Matrix-Product-State Decomposition </center> </big> </h1>\n",
    "<HR> $$\\newcommand{\\ket}[1]{\\left|{#1}\\right\\rangle} \\newcommand{\\bra}[1]{\\left\\langle{#1}\\right|} $$\n",
    "First of all we introduce a random state in the hilbert-space of N spins\n",
    "    \\begin{equation}\n",
    "    \\ket{\\psi} = \\sum\\limits_\\vec{\\sigma}c_\\vec{\\sigma} \\ket{\\vec{\\sigma}}\n",
    "    \\end{equation}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "polar-issue",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import numpy.linalg as LA\n",
    "import matplotlib.pyplot as plt\n",
    "from ncon import ncon\n",
    "from scipy.sparse.linalg import svds\n",
    "import ncon"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "rough-multimedia",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Number of lattice sites\n",
    "N = 6\n",
    "# Local Hilbert-Space dimension\n",
    "d = 2 \n",
    "# Hilbert-Space dimension\n",
    "dim = 2**N\n",
    "\n",
    "uparrow = '\\u2191'\n",
    "downarrow = '\\u2193'\n",
    "\n",
    "basis = np.vectorize(np.binary_repr)(np.arange(0,2**N),width=N)\n",
    "basis = np.vectorize(np.char.replace)(basis, '0', uparrow)\n",
    "basis = np.vectorize(np.char.replace)(basis, '1', downarrow)\n",
    "\n",
    "c = np.random.rand(dim) + 1j*np.random.rand(dim)\n",
    "c = c/LA.norm(c)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "adequate-tanzania",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "['↑↑↑↑↑↑' '↑↑↑↑↑↓' '↑↑↑↑↓↑' '↑↑↑↑↓↓' '↑↑↑↓↑↑' '↑↑↑↓↑↓' '↑↑↑↓↓↑' '↑↑↑↓↓↓'\n",
      " '↑↑↓↑↑↑' '↑↑↓↑↑↓' '↑↑↓↑↓↑' '↑↑↓↑↓↓' '↑↑↓↓↑↑' '↑↑↓↓↑↓' '↑↑↓↓↓↑' '↑↑↓↓↓↓'\n",
      " '↑↓↑↑↑↑' '↑↓↑↑↑↓' '↑↓↑↑↓↑' '↑↓↑↑↓↓' '↑↓↑↓↑↑' '↑↓↑↓↑↓' '↑↓↑↓↓↑' '↑↓↑↓↓↓'\n",
      " '↑↓↓↑↑↑' '↑↓↓↑↑↓' '↑↓↓↑↓↑' '↑↓↓↑↓↓' '↑↓↓↓↑↑' '↑↓↓↓↑↓' '↑↓↓↓↓↑' '↑↓↓↓↓↓'\n",
      " '↓↑↑↑↑↑' '↓↑↑↑↑↓' '↓↑↑↑↓↑' '↓↑↑↑↓↓' '↓↑↑↓↑↑' '↓↑↑↓↑↓' '↓↑↑↓↓↑' '↓↑↑↓↓↓'\n",
      " '↓↑↓↑↑↑' '↓↑↓↑↑↓' '↓↑↓↑↓↑' '↓↑↓↑↓↓' '↓↑↓↓↑↑' '↓↑↓↓↑↓' '↓↑↓↓↓↑' '↓↑↓↓↓↓'\n",
      " '↓↓↑↑↑↑' '↓↓↑↑↑↓' '↓↓↑↑↓↑' '↓↓↑↑↓↓' '↓↓↑↓↑↑' '↓↓↑↓↑↓' '↓↓↑↓↓↑' '↓↓↑↓↓↓'\n",
      " '↓↓↓↑↑↑' '↓↓↓↑↑↓' '↓↓↓↑↓↑' '↓↓↓↑↓↓' '↓↓↓↓↑↑' '↓↓↓↓↑↓' '↓↓↓↓↓↑' '↓↓↓↓↓↓']\n",
      "[0.018+0.06j  0.043+0.087j 0.141+0.022j 0.065+0.017j 0.113+0.085j\n",
      " 0.122+0.107j 0.132+0.035j 0.13 +0.075j 0.012+0.038j 0.142+0.087j\n",
      " 0.145+0.093j 0.147+0.093j 0.126+0.093j 0.137+0.138j 0.081+0.073j\n",
      " 0.043+0.004j 0.037+0.117j 0.003+0.014j 0.14 +0.077j 0.139+0.115j\n",
      " 0.095+0.03j  0.088+0.062j 0.076+0.13j  0.07 +0.043j 0.029+0.057j\n",
      " 0.138+0.098j 0.038+0.097j 0.032+0.14j  0.01 +0.117j 0.141+0.052j\n",
      " 0.135+0.089j 0.016+0.084j 0.076+0.092j 0.022+0.093j 0.124+0.018j\n",
      " 0.08 +0.045j 0.004+0.107j 0.037+0.039j 0.086+0.128j 0.021+0.119j\n",
      " 0.04 +0.046j 0.01 +0.133j 0.071+0.093j 0.064+0.108j 0.04 +0.077j\n",
      " 0.117+0.051j 0.133+0.049j 0.061+0.105j 0.029+0.044j 0.075+0.114j\n",
      " 0.091+0.1j   0.022+0.137j 0.083+0.084j 0.14 +0.104j 0.112+0.141j\n",
      " 0.071+0.082j 0.132+0.059j 0.025+0.003j 0.083+0.053j 0.045+0.095j\n",
      " 0.006+0.049j 0.1  +0.148j 0.018+0.113j 0.045+0.038j]\n",
      "(64,)\n"
     ]
    }
   ],
   "source": [
    "# Just to fix the ideas\n",
    "print(basis)\n",
    "print(np.round(c,3))\n",
    "print(c.shape)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "protected-wells",
   "metadata": {},
   "source": [
    "<h2>1. Left canonical decomposition of a state</h2>\n",
    "<HR>\n",
    "<h3>1.1 Single Value Decomposition</h3>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "lonely-universe",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Should be zero:  8.173171517933779e-15\n",
      "Should be one:   1.000000000000001\n"
     ]
    }
   ],
   "source": [
    "# We initialize again the coefficients of the chain\n",
    "N   = 16\n",
    "dim = d**N\n",
    "c = np.random.rand(dim)+1j*np.random.rand(dim)\n",
    "#for i in np.arange(dim):\n",
    "#    if(bin(i).count('1')==N//2): c[i] = 0.\n",
    "c = c/LA.norm(c)\n",
    "\n",
    "# Save the configuration in order \n",
    "# to check the algorithm\n",
    "c_check = c.copy()\n",
    "\n",
    "# At every step A are a set of\n",
    "# d matrices of dimension (r1 x r2)\n",
    "A   = []\n",
    "r1  = 1\n",
    "for i in range(1,N+1):\n",
    "    c = c.reshape(r1*d, d**(N-i))\n",
    "    U, S, V = LA.svd(c,full_matrices=False)\n",
    "    r2 = S.size\n",
    "    A.append(U.reshape(d,r1,r2,order='F'))\n",
    "    r1 = r2\n",
    "    c  = (np.diag(S)@V)\n",
    "\n",
    "res = A[0]\n",
    "for i in range(1,N):\n",
    "    res = np.tensordot(res,A[i],axes=[[i+1],[1]])\n",
    "res = np.squeeze(res)\n",
    "res_check = res.reshape(d**N)\n",
    "print('Should be zero: ',LA.norm(c_check-res_check))\n",
    "print('Should be one:  ',LA.norm(res_check))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "spoken-wireless",
   "metadata": {},
   "source": [
    "<h2> Left Nomalization </h2>\n",
    "\n",
    "$$\\sum_{\\sigma_l} A^\\dagger_{\\sigma_l} A_{\\sigma_l} = \\mathbb{I}$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "settled-bread",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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mlpyqTyTo4DKzBdzHZWZJcnCZWXIcXGaWHAeXmSXHwWVmSSlzIsF+cXCZWQO3uMxGyCBnlRjmjBIOLjNLjoPLzJKSwgDUInPOb5N0QtL+JsveLykkLetP9cxsGKp+Q9gi91W8HZiof1PSSrJbDh0puU5mNmQnT54s9BiWtsEVEfcDTzZZ9LfAB2gx8b2ZpavqLa5u76t4NfBYRDzc7sxHfrui+lsWmVlFDTuUiug4uCQtAW4E3lhk/YiYIrszraduNkvEyAUX8HJgNXCqtbUCeEjS2oj4YZmVM7PhGLngioh9wLmnXkv6ATAeEXMl1svMhqjql/wUGQ5xF/At4AJJs5Ku63+1zGxYinbMV7pzPiI2tlm+qrTamFkljNyhopmNPgeXmXV1wXQ34TE+Xs69WR1cZpYcB5eZJcUTCZpZktziMrPkOLjMLDkOLjNLyrAHlxbh4DKzBg4uM0uOzyqaWXLc4jKzpKTQx1VkznkzO82UOTuEpAlJhyTNSNrSZLkkfSpfvlfSxe3KdHCZWYOygkvSGHAzcCVwIbBR0oV1q10JrMkfk8At7cp1cJlZgxLv8rMWmImIwxHxDLAdWF+3znrgs5F5ADhb0nmLFTroPq454L9bLFuWLx8212Mh12OhgdWjzYwSrerx0hI2fU9efhHPkrS75vVUfp+JU5YDR2tezwKX1JXRbJ3lwPFWGx1ocEXEOa2WSdodEeXMydED18P1ON3rEREN91HtQbP0rT/GLLLOAj5UNLN+mgVW1rxeARzrYp0FHFxm1k+7gDWSVks6C9gA7KhbZwfwzvzs4qXAjyOi5WEiVGsc11T7VQbC9VjI9VjI9ehARMxL2kzWbzYGbIuIA5I25cu3AjuBdcAM8DRwbbtyVfWBZmZm9XyoaGbJcXCZWXIGGlz9GPrfRR1WSvq6pIOSDki6vsk6l0n6saQ9+eNDZdejZls/kLQv387uJsv7uk8kXVDz79wj6SlJ76tbp2/7Q9I2SSck7a9574WS7pP03fzvC1p8dtHfUwn1uEnSd/L9/gVJZ7f47KLfYQn1+Iikx2r2/7oWny1tf1ReJ3et7eVB1jH3PeBlwFnAw8CFdeusA75CNq7jUuDBPtTjPODi/PlS4NEm9bgM+PKA9ssPgGWLLO/7Pqn7jn4IvHRQ+wN4PXAxsL/mvb8CtuTPtwAf6+b3VEI93gickT//WLN6FPkOS6jHR4D3F/juStsfVX8MssXVl6H/nYqI4xHxUP78J8BBslG6VdX3fVLjcuB7EdHq6obSRcT9wJN1b68H7sif3wG8qclHi/yeeqpHRNwbEfP5ywfIxhf1VYv9UUSp+6PqBhlcrYb1d7pOaSStAl4FPNhk8aslPSzpK5J+s191IBshfK+kaUmTTZYPcp9sAO5qsWxQ+wPgxZGP48n/nttknYH+VoB3k7V8m2n3HZZhc37Iuq3FofOg98dQDTK4+jL0v1uSngt8HnhfRDxVt/ghssOli4C/A77YjzrkXhsRF5NdIf8eSa+vr2qTz5S+T/LBgVcD/9pk8SD3R1GD/K3cCMwDd7ZYpd132KtbgJcDv0V2/d7fNKtmk/dGdqzTIIOrL0P/uyHpTLLQujMi7q5fHhFPRcT/5s93AmdKKnrRaUci4lj+9wTwBbImf62B7BOy/3QPRcTjTeo4sP2Re/zU4XD+90STdQb1W7kGuAp4W+SdSfUKfIc9iYjHI+IXEXES+PsW5Q/qd1IJgwyuvgz975QkAbcBByPi4y3W+dV8PSStJdtPPyqzHnnZz5G09NRzss7g/XWr9X2f5DbS4jBxUPujxg7gmvz5NcCXmqxT5PfUE0kTwA3A1RHxdIt1inyHvdajtk/zzS3K7/v+qJRBngkgO0P2KNnZjxvz9zYBm/LnIpt07HvAPmC8D3V4HVkTei+wJ3+sq6vHZuAA2ZmZB4DX9Gl/vCzfxsP59oa1T5aQBdHza94byP4gC8vjwM/JWg3XAS8CvgZ8N//7wnzdlwA7F/s9lVyPGbJ+o1O/k6319Wj1HZZcj3/Mv/u9ZGF0Xr/3R9UfvuTHzJLjkfNmlhwHl5klx8FlZslxcJlZchxcZpYcB5eZJcfBZWbJ+X/30Lzt7hnnlgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "## Normalization condition\n",
    "for i in range(N):\n",
    "        plt.figure()\n",
    "        plt.imshow(np.round(A[i][0,:,:].T.conjugate()@A[i][0,:,:]+A[i][1,:,:].T.conjugate()@A[i][1,:,:]).real, cmap=plt.cm.gray)\n",
    "        plt.colorbar()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "frozen-transport",
   "metadata": {},
   "source": [
    "<center><h1><big>QR-decomposition</big></h1></center>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 271,
   "id": "opened-complexity",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Should be zero:  9.014290380483908e-16\n",
      "Should be one:   1.0\n"
     ]
    }
   ],
   "source": [
    "# We initialize again the coefficients of the chain\n",
    "N   = 10\n",
    "dim = d**N\n",
    "c = np.random.rand(dim)+1j*np.random.rand(dim)\n",
    "#for i in np.arange(dim):\n",
    "#    if(bin(i).count('1')==N//2): c[i] = 0.\n",
    "c = c/LA.norm(c)\n",
    "\n",
    "# Save the configuration in order \n",
    "# to check the algorithm\n",
    "c_check = c.copy()\n",
    "\n",
    "# At every step A are a set of\n",
    "# d matrices of dimension (r1 x r2)\n",
    "A   = []\n",
    "r1  = 1\n",
    "for i in range(1,N+1):\n",
    "    c = c.reshape(r1*d, d**(N-i))\n",
    "    Q, c = LA.qr(c)\n",
    "    r2 = c.shape[0]\n",
    "    A.append(Q.reshape(d,r1,r2,order='F'))\n",
    "    r1 = r2\n",
    "\n",
    "res = A[0]\n",
    "for i in range(1,N):\n",
    "    res = np.tensordot(res,A[i],axes=[[i+1],[1]])\n",
    "res = np.squeeze(res)\n",
    "res_check = res.reshape(d**N)\n",
    "\n",
    "print('Should be zero: ',LA.norm(c_check-res_check))\n",
    "print('Should be one:  ',LA.norm(res_check))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 272,
   "id": "sensitive-mercury",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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MUuvDyfZPgRf2uS4RMWCtD6eIGD2Z+BsRxUo4RUSRRuVuXUSMmLScIqI4pfc51R4hHhGjp6kR4pKmJJ2QNCtp7zLHJelD1fGHJV3Vq8yEU8QYayKcqtVKbqMzi+QKYLekK5acdgOwvXrsAW7vVbeEU8QYW1hYqPXoYQcwa/uk7bPAQWDnknN2Ah9zxwPAxZIuXa3QfvU5zQNrXVZlY/W+UTSq3y3fa4kBbn/+Kw2UcS+d71rHcyUd7Xo+bXu6+nkTcKrr2Bxw9ZL3L3fOJuCJlT6wL+Fk+5K1vkfS0VFd0WBUv1u+V7vZnmqoqOUSeem1YJ1zfk4u6yJiveaALV3PNwOnn8U5PyfhFBHrdQTYLmlbte7bLuDQknMOAW+t7tq9Avih7RUv6aCscU7TvU9prVH9bvlege1zkm6l04c1ARywfUzSLdXxfcBh4EZgFvgpcHOvclXyIKyIGF+5rIuIIiWcIqJIRYRTr6HvbSRpi6QvSjou6Zikdw67Tk2SNCHp65I+O+y6NEnSxZLulvR49bt75bDrNK6G3udUDX3/Bp1lgOfo9Pzvtv3YUCu2TtXo10ttPyjpQmAG+MO2f69Fkv4cmAQusn3TsOvTFEkfBb5se39152mD7R8MuVpjqYSWU52h761j+wnbD1Y//xg4TmdEbOtJ2gy8Htg/7Lo0SdJFwKuBOwBsn00wDU8J4bTSsPaRIWkrcCXwtSFXpSkfBN4NlLtS2bPzEuB7wEeqS9b9kp4/7EqNqxLCac3D2ttE0guATwPvsv2jYddnvSTdBJyxPTPsuvTBecBVwO22rwSeBEaiD7SNSginNQ9rbwtJ59MJprts3zPs+jTkGuANkr5F5xL8WkkfH26VGjMHzNlebOHeTSesYghKCKc6Q99bR53p6XcAx21/YNj1aYrt99rebHsrnd/VF2y/ecjVaoTt7wKnJF1evXQdMBI3MNpo6NNXVhr6PuRqNeEa4C3AI5Ieql77S9uHh1elqOEdwF3V/yhPUmOaRfTH0IcSREQsp4TLuoiIZ0g4RUSREk4RUaSEU0QUKeEUEUVKOEVEkRJOEVGk/wcjtfFRfc5+QAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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AsJ6uKaK2v9dVfjtw7kyVJuQiorZZhNxySTu7Po9Xs5ygM+f9xa5jk0zfS/s48OhMDSbkIqK2WYTcYduDJsz2exStb8WS/oJOyP3JTA0m5CKilgYfBp4EVnV9PpfOgh6vI+mPgK8Ca23POHMqo6sRUVtDo6s7gBFJF0g6HdgAbOkuIOk84CHgets/Gubc0pOLiNqaGF21PSXpVuAxYAmwyfY+STdVxzcCtwO/A3ylWtZraprLXyAhFxENaOph4GqVoq09323sev8J4BOzqTMhFxG1FD9BPyIiIRcRRUvIRUTRSl80MyIWsdyTi4jiJeQiomhtDrnaMx4kvVXSDyQ9LWmfpC/0KSNJd1RrRO2VdGnddiOiPYrerQv4FXB1tafqUuBJSY/a3t5VZi2dfVZH6KwqcDczrAEVEQtHm3tyTWxkY+BY9XFp9er9idcDm6uy2yUtk7TC9sG67UfE/Gpq0cxTpanNpZdU2xEeArbZfqqnSL91olY20XZEzL82X642EnK2X7N9MZ2lUVZLendPkdmsEzUmaWfPwnoR0WLFh9wJtn8GfBdY03NoqHWiqjrGbY/OtLJARLRH0SEn6WxJy6r3bwPeD/ywp9gW4IZqlPVy4Ejux0WUYdiAW8ijqyuAe6uddt4CfN32Iz1rQG0F1gETwCvAjQ20GxEtUfro6l7gkj7fd68BZeCWum1FRDu1eXQ1Mx4ioraie3IRsbhlgn5EFC8hFxFFS8hFRNEy8BARxco9uYgoXkIuIoqWkIuIoiXkIqJoCbmIKFbbF81MyEVEbenJRUTREnIRUbSEXEQUKw8DR0TxEnIRUbSMrkZE0dKTi4hitf2eXBO7db1V0g8kPS1pn6Qv9ClzlaQjkvZUr9vrthsR7dHUbl2S1kh6XtKEpNv6HJekO6rjeyVdOlOdTfTkfgVcbfuYpKXAk5Ietb29p9wTtq9poL2IaJkmenLVjn93AR+gs1fzDklbbD/XVWwtMFK9LgPurn4dqHZPzh3Hqo9Lq1d7+64R0bjjx48P9ZrBamDC9gu2fw08AKzvKbMe2FzlznZgmaQV01XayD25KoF3AX8A3GX7qT7FrpD0NHAA+IztfQPqGgPGqo/HgOebOMchLAcOz1Fbcyk/VwMkzVVTMLc/2/kN1PEYnXMexlsl7ez6PG57vHq/Enix69gkb+yl9SuzEhi4WX0jIWf7NeBiScuAb0h6t+1nu4rsBs6vLmnXAQ/T6W72q2scGO937FSStNP26Fy3e6rl51p4FtrPZntNQ1X1+z9J71XhMGVep/bl6utasn8GfBdY0/P90ROXtLa3AkslDZv8EbE4TAKruj6fS+fKb7ZlXqeJ0dWzqx4ckt4GvB/4YU+Zc1T19yWtrtp9qW7bEVGUHcCIpAsknQ5sALb0lNkC3FCNsl4OHLE98FIVmrlcXQHcW92XewvwdduPSLoJwPZG4FrgZklTwKvABrfvwZo5v0SeI/m5Fp6Sf7aBbE9JupXOPb4lwCbb+3qyZCuwDpgAXgFunKletS9rIiKa0+g9uYiItknIRUTRFn3IzTSNZKGStEnSIUnPzlx64ZC0StJ3JO2vphF+cr7PqQnDTI+MN2dR35OrBkt+RNc0EuC6nmkkC5KkP6PzMPVm2++e7/NpSvV0+wrbuyWdRech9A8t9P9m1dMHZ3RPjwQ+2Wd6ZMzSYu/JDTONZEGy/Tjw8nyfR9NsH7S9u3r/c2A/nSfeF7RMjzx1FnvIDZoiEguApHcAlwD9phEuOJKWSNoDHAK2DZgeGbO02ENu1lNEoh0knQk8CHzK9tH5Pp8m2H7N9sV0nuJfLamY2wzzabGH3KyniMT8q+5ZPQjcZ/uh+T6fpg2aHhlvzmIPuWGmkUSLVDfovwbst/2l+T6fpgwzPTLenEUdcrangBPTSPbTmZLWdwmohUbS/cD3gXdKmpT08fk+p4ZcCVwPXN210vS6+T6pBqwAviNpL53/+W6z/cg8n1MRFvUjJBFRvkXdk4uI8iXkIqJoCbmIKFpCLiKKlpCLiKIl5CKiaAm5iCja/wOPiiHQpsPJyAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "## Normalization condition\n",
    "for i in range(N):\n",
    "        plt.figure()\n",
    "        plt.imshow(np.round(A[i][0,:,:].T.conjugate()@A[i][0,:,:]+A[i][1,:,:].T.conjugate()@A[i][1,:,:]).real, cmap=plt.cm.gray)\n",
    "        plt.colorbar()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "chronic-patent",
   "metadata": {},
   "source": [
    "<h2> Right Canonical decomposition </h2>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "helpful-sample",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(2, 1, 2) (2, 2, 1)\n",
      "(2, 1, 2) (2, 2, 4)\n",
      "(2, 1, 2, 4) (2, 4, 8)\n",
      "(2, 1, 2, 2, 8) (2, 8, 16)\n",
      "(2, 1, 2, 2, 2, 16) (2, 16, 32)\n",
      "(2, 1, 2, 2, 2, 2, 32) (2, 32, 64)\n",
      "(2, 1, 2, 2, 2, 2, 2, 64) (2, 64, 128)\n",
      "(2, 1, 2, 2, 2, 2, 2, 2, 128) (2, 128, 256)\n",
      "(2, 1, 2, 2, 2, 2, 2, 2, 2, 256) (2, 256, 128)\n",
      "(2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 128) (2, 128, 64)\n",
      "(2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 64) (2, 64, 32)\n",
      "(2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 32) (2, 32, 16)\n",
      "(2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 16) (2, 16, 8)\n",
      "(2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 8) (2, 8, 4)\n",
      "(2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 4) (2, 4, 2)\n",
      "(2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2) (2, 2, 1)\n",
      "Should be zero:  1.4081879434164186\n",
      "Should be one:   0.9920678002044759\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# We initialize again the coefficients of the chain\n",
    "N   = 16\n",
    "dim = d**N\n",
    "c = np.random.rand(dim)#+1j*np.random.rand(dim)\n",
    "c = c/LA.norm(c)\n",
    "\n",
    "# Save the configuration in order \n",
    "# to check the algorithm\n",
    "c_check = c.copy()\n",
    "\n",
    "# At every step A are a set of\n",
    "# d matrices of dimension (r1 x r2)\n",
    "B   = []\n",
    "r1 = 1\n",
    "for i in range(1,N+1):\n",
    "    c = c.reshape(d**(N-i),r1*d)\n",
    "    U, S, V = LA.svd(c, full_matrices=False)\n",
    "    r2 = S.size\n",
    "    B.append(V.reshape(d,r2,r1))\n",
    "    r1 = r2\n",
    "    c  = (U@np.diag(S).T)\n",
    "\n",
    "B.reverse()\n",
    "print(B[0].shape,B[-1].shape)\n",
    "res = B[0]\n",
    "for i in range(1,N):\n",
    "    print(res.shape,B[i].shape)\n",
    "    res = np.tensordot(res,B[i],axes=[[i+1],[1]])\n",
    "res = np.squeeze(res)\n",
    "res = res.reshape(d**N)\n",
    "\n",
    "plt.plot(res)\n",
    "plt.plot(c_check)\n",
    "\n",
    "print('Should be zero: ',LA.norm(c_check-res))\n",
    "print('Should be one:  ',LA.norm(res))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 262,
   "id": "noted-battlefield",
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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vlz179nxa086Kd5pkEM/Cm4k04ESnqo+r6kRVvYJQ9YDfqeqDhKoIrHE2WwPYnbAD4PP52LFjB8FgkNtuu43Ro0fjFHIwxlWp2KIbjKG9nwCviMha4DTwpUE4R8Z49913qaurY9asWcyZM4fKykoCgYDbYZkMloyJLJK4JDpVfRN40/ncCCyOx3FNqHinz+djzpw5FBQUUFRUhN/vp7m52e3QTIbK2ERnBpeqUllZSVFREStWrOD48eNs3rzZ7bBMhkrFRGc3aqWIQCCA3+/n+PHjBAIBZs+ezejR9tCJSayMG4wwidfc3MzmzZtpbGykrKyMCRP6nPjImEGRioMRluhS0KlTp3j11VcpKSlh+fLljBw50u2QTAaxRGcSoqmpiSNHjpCdnc2UKVPIy8tj+PDhbodlMkS8Ep2IPCMi9SJypJf1q0XksPPaLSLXh62rFZF3ReSQiFRFOpcNRqSwHTt2UFVVxfLly2lsbGT9+vVuh2TSXJxbbM8SmhPiV72s/xOwSFWbRGQpsA6YH7b+dlVtiOZEluhSWEtLCx0dHTQ2NhIMBrnqqqtoaGjA4/G4HZpJY/FKdKq6S0Su6GP97rCvewjN3zog1nVNce3t7axfv57q6mpWrlzJ1Vdf7XZIJs1FOepaLCJVYa9YC3isBcLvqVLgDRHZH82xrUWXJhoaGti2bRs5OTksXryYffv2WdUTE3f96Lo2xKtgh4jcTijRhc/+fouqnnWqI20TkWpV3dXbMaxFlyY8Hg979uwhKyuLefPmkZ+fT1ZWltthmTSUyFFXEZlFqN5lmfPUVVcMZ533euB14Ma+jmMtujTzzjvvUF1dzcKFCwkEAlRUVNDR0eF2WCaNJOr2ERG5HHgN+Iqqvh+2PBcYoqp+5/MS4Ed9HcsSXZrx+/20tLQQCATIzs6mpKQEn89n3VgTN/FKdCLyInAboet5dcAPgWHOOZ4CfgCMAX7mVO4JOt3hccDrzrKhwAuquqWvc1miS0MdHR1UVFRQUlLC6tWr2b9/P7/97W/dDsukga5HwOJ0rJUR1n8d+HoPy08C1//lHr2za3RpqqOjA6/XS1VVFcFgkAULFti8sSYu7MkIk1T8fj/bt2+nra2NJUuWUFxc7HZIJg2kYqKzrmsGqK6upqGhgenTpzNz5kw2b95Me3u722GZFJWMiSwSa9FlAI/HQ01NDUOHDqW4uJjCwkIrBGAGzFp0Jqlt2bKFwsJCvvSlL1FbW8vGjRvdDsmkmGRNZJFYiy6DtLe34/f7qa2tpb29nZkzZ1rxTtNvVnjTJL2WlhY2btzIuXPn+OIXv8jkyZPdDsmkmFTsulqiy1B1dXWUl5czZswYli5dSm5urtshmRRhic6kDI/Hw6FDh8jOzmb69Onk5eWRnZ3tdlgmyUWT5JIx0dlgRIbbtWsXBw8epLS0FK/Xy/r165PyF9Ukj1T8/bBEl+Gam5u5ePEiHo8HVWXy5Mk0NTXh9XrdDs0kqVRMdNZ1NQQCAcrLy/njH//Igw8+yHXXXed2SCaJZdyoq4gUishvRKRaRI6JyE0iUiQi20TkA+fd7l9IAapKU1MTb775JkOHDuW2224jPz/f7bBMkknVa3SxtuieBLao6tWEqgkcAx4DtqvqVGC7892kAK/Xy+9//3sAbrrpJgoLCxkyxBr95lIZlehEJB/4PPBLAFUNqKoHKAOeczZ7Drg3thBNoh04cIDnn3+ez33uc5SVlTF0qF3KNX+WUYkOuBL4GPhfETkoIr9wqn2OU9VzAM772J52FpGHuybOiCEGMwh8Ph91dXV0dnYycuRIxo4dy6hRo9wOyySJTEt0Q4G5wM9VdQ7QTD+6qaq6TlXnaZwm0DDx1dnZyYYNG/jd737HqlWruPnmm90OySSBrsKbmTQYUQfUqepe5/tvCCW+j0SkBMB5r48tROOWYDCI3+/n8OHDXLx4kXnz5lnxTpNZLTpVPQ+cEZHpzqLFwHtABbDGWbYGKI8pQuOqCxcu8MYbb+D3+7nrrru47LLL3A7JuCxeiU5EnhGRehE50st6EZH/FpEaETksInPD1pWKyHFnXcSeZKxDat8BnheRw8Bs4MfAT4A7ROQD4A7nu0lxNTU1vPTSS0yZMoWysjJycnLcDsm4JI4tumeB0j7WLwWmOq+HgZ8DiEgW8FNn/TXAShG5pq8TxTScpqqHgJ6usS2O5bgm+Xg8HjweD9OnT6ekpISCggJEhNbWVrdDMwkWr66pqu4SkSv62KQM+JWGTrjHuW+3BLgCqNHQJDmIyEvOtu/1diC7b8D0yxtvvEFBQQF//dd/zYcffkhFRYXbIZkE6keLrbjbHRXrVHVdP083ATgT9r3OWdbT8vl9HcgSnemXtrY2AD788EMCgQBXX30158+fx+PxuBuYSZgoR1Ub4nBHhfSwTPtY3iu77d30W1tbGxUVFdTW1vLlL3+Zq666yu2QTAIlcNS1DpgU9n0icLaP5b2yRGcG7Pz581RWVpKXl8edd95pNxVniAQmugrgq87o6wLA6zyEsA+YKiJTRCQbWOFs2ytLdGbAPB4PVVVVZGdnM3PmTPLy8uxxsTQXz4f6ReRF4G1guojUichaEXlERB5xNtkEnARqgKeBbzoxBIFvA1sJPV//iqoe7etc9ltpYvaHP/yBw4cPs3jxYpqbmykvL0/Ku+NNfMRx1HVlhPUKfKuXdZsIJcKoWKIzMbtw4QJtbW00NzcDMGnSJDwejxXvTFPJ+ORDJNZ1NXERDAYpLy/nwIEDrFq1ijlz5rgdkhkkmfasqzGX6OzsxOPxsHv3bgA+//nPU1BQ4HJUJp4ytfCmMZfwer3s3LmTYDDIrbfeyujRoxHp6bYnk6pSMdHZNTozKN59913q6uqYPXs2c+bMYePGjVy8eNHtsEwcJGMii8RadGZQeL1eTp06hYiQl5dHcXGx3WeXJqxFZ0wYVWXjxo2MGTOGlStXUl1dzebNm90Oy8Sgq/BmqrEWnRlUFy9exO/3U11dTSAQYPbs2YwebRPDpbJUbNFZojODrrm5mc2bN9PY2EhZWRnjx493OyQTA0t0xvShtraW3/zmN0yYMIG7776bESNGuB2SGYBUTHR2jc4kTFfxzilTpnD55ZeTn59PZ2cn7e3tbodm+iEZE1kkluhMwm3fvp38/Hzuuece6uvrKS+3aUVSRbK22CKxRGcSrrW1lc7OTurr6wkEAkybNo36+nor3pkibNTVmCi1t7dTXl7OBx98wIoVK5g+fXrknUxSSMVrdJbojKsaGhrYunUrI0aM4I477iAvL8/tkEwEluiM6SePx8PevXsZOnQoc+bMIT8/34p3JrFUfajffqNMUti7dy/Hjh3j1ltvpb29nYqKCjo6OtwOy/QgGRNZJJboTFLw+/20tLTQ3t7O0KFDKSkpwefz4fP53A7NdJOKic66riZpdHR0UFFRwdtvv82DDz7IDTfc4HZIpgfxKrwpIqUiclxEakTksR7Wf09EDjmvIyLSISJFzrpaEXnXWVf1l0e/VEyJTkT+VkSOOkG8KCI5IlIkIttE5APn3R5sNFHr6OjA5/Oxd+9eVJWbb76ZwsJCt8MyjnhdoxORLOCnwFLgGmCliFzT7Vz/pqqzVXU28DiwU1U/Cdvkdmd9xPljB5zoRGQC8CgwT1VnAlmEph17DNiuqlOB7c53Y6Lm8/nYsWMHgUCAxYsXM2bMGCvemUTiNBhxI1CjqidVNQC8BJT1sf1K4MWBxhxr13UoMEJEhgIjCU0iWwY856x/Drg3xnOYDHX06FFeeOEFrrnmGsrKysjOznY7JEPUia5YRKrCXg93O8wE4EzY9zpn2V8QkZFAKfBqeBjAGyKyv4dj/4UBD0ao6oci8u/AaaAVeENV3xCRcRqaZBZVPSciY3sJ/mEgYoAmc3m9Xnw+H9dddx2jR4+mqKgIn89HS0uL26FltChbbA0RupQ9NdF7O/DdwB+6dVtvUdWzTn7ZJiLVqrqrt5PF0nUdTaj1NgUYD+SKyIPR7q+q61R1XjT9a5O5VJVNmzaxefNmHnjgAW6//Xa3Q8poXYU34zAYUQdMCvs+kVCPsCcr6NZtVdWzzns98DqhrnCvYum6/hXwJ1X9WFUvAq8BNwMfiUgJgPNeH8M5jCEQCODz+Thx4gTt7e3MmjXLine6KE7X6PYBU0VkiohkE0pmFd03EpECYBFQHrYsV0Tyuj4DS4AjfZ0slkR3GlggIiMldKV4MXDMCXaNs82a8ACNGaiWlhYqKyupr6/nvvvuY9KkSZF3MoMiHolOVYPAt4GthPLGK6p6VEQeEZFHwja9j9BlseawZeOA34vIH4F3gEpV3dLX+SSWm/9E5P8AXwaCwEHg68Ao4BXgckLJ8Evd+tY9HSf17kA0rigsLOTyyy9n7NixDB8+nDfffJPm5ubIOxqA/bFeKhozZoyWlpZG3O6FF16I+VzxFNOoq6r+UFWvVtWZqvoVVW1X1UZVXayqU533PpOcMf3h8Xg4fPgww4cP56qrriIvL89GYxPMnnU1JkF27NhBVVUVy5Yto6mpifLy8qT8B5ZukjWRRWKJzqSklpYWgsEgTU1NdHR0cOWVV9LY2GjFOxPACm8ak0CBQIDy8nLee+89Vq1axbXXXut2SBkhFbuuluhMSlNVGhoa2L59O8OGDeP2228nPz/f7bDSmiU6Y1zg9XrZvXs3IsL8+fMpKCggKyvL7bDSUrwe6k80u0Zn0sb+/fupqalhwYIFBINBNmzYQDAYdDustJOMiSwSS3Qmbfh8PpqbmwkGg+Tk5DBu3Dh8Ph9+v9/t0NKKDUYY47KOjg42bNjAzp07Wb16NQsWLHA7pLSSql1XS3Qm7QSDQfx+PwcPHiQYDDJ//nwr3hlHluiMSRJ+v59t27bR0tLCnXfeydixPVYLMwOQionOrtGZtHb8+HGampr47Gc/y4wZM9i6dSttbW1uh5XSkjGRRWItOpPWPB4P77//PtnZ2YwbN46CggJGjBjhdlgpzVp0xiSpLVu2UFhYyP3338+ZM2eoqPiL0mcmCl2FN1ONtehMRmhvb8fn83H69Gna29u59tprrXjnAKVii84SnckYra2tbNiwgTNnznD//fczZcoUt0NKSZbojEkBZ8+eZcOGDRQUFFBaWkpubq7bIaUUS3TGpACPx8OBAwcYPnw4M2bMID8/n2HDhrkdVkqwG4aNSTFvvfUWL774InfccQfLly+3SbKjFK9EJyKlInJcRGpE5C8muheR20TEKyKHnNcPot23Oxt1NRmrubmZQCCA3+9HVZk8eTJNTU14vV63Q0tq8Rh1FZEs4KfAHYSmPtwnIhWq+l63Td9S1eUD3PdT1qIzGe3ixYusX7+eQ4cOsXr1aq6//nq3Q0p6cWrR3QjUqOpJVQ0ALxGaJ3pQ9rVEZzKeqtLU1MRbb73FkCFDWLRoEQUFBW6HlZT6cY2uWESqwl4PdzvUBOBM2Pc6Z1l3N4nIH0Vks4h0lZCOdt9PWaIzhlDxzl27dqGqLFy4kMLCQoYMsX8ePYky0TWo6ryw17puh+npgmj3puABYLKqXg/8X2B9P/a9hP0kjQlz6NAhfv3rXzN37lzKyspsNLYHceq61gHhs5BPBM52O49PVS84nzcBw0SkOJp9u7NEZ0wYr9fLmTOhXlFubi7FxcWMGjXK5aiSS2dnZ8RXFPYBU0VkiohkAyuAS57LE5HLxBkKF5EbCeWrxmj27c5GXY3pprOzk40bN1JcXMyqVas4evQoW7ZscTuspBCv++RUNSgi3wa2AlnAM6p6VEQecdY/BdwPfENEgkArsEJDJ+9x377OJ5GCFpFngOVAvarOdJYVAS8DVwC1wAOq2uSsexxYC3QAj6rq1kh/aBFJvjsMTcYbNWoUt9xyy6e3oJw4cYKmpia3w4rFflWdF8sBRo0apdGMTO/evTvmc8VTNF3XZ4HSbsseA7ar6lRgu/MdEbmGUDPyWmefnzn3vBiTci5cuMDWrVvx+XzcddddjBs3zu2QkkJaPhmhqruAT7otLgOecz4/B9wbtvwlVW1X1T8BNYTueTEmZZ04cYKXX36ZyZMnc88992R8Pbu0THS9GKeq5wCc96461VHf3yIiD3fdYzPAGIxJCI/HQ3V1NcOHD2fChAnk5+eTk5PjdliuScVEF+/BiKjvb3Huq1kHdo3OpIZt27aRn5/Pvffey/nz5ykvL3c7pITTDCu8+ZGIlAA47/XO8n7f32JMqmhtbcXr9XLu3DkCgQDTp0/PyNnFUrFFN9BEVwGscT6vAcrDlq8QkeEiMgWYCrwTW4jGJI+2tjYqKio4efIkK1asYNq0aW6HlHBpmehE5EXgbWC6iNSJyFrgJ8AdIvIBoQoCPwFw7mV5BXgP2AJ8S1U7Bit4Y9zy0UcfUVlZSW5uLkuWLCEvL8/tkBImFRNdxGt0qrqyl1WLe9n+n4F/jiUoY5Kdx+OhqqqKJUuWMGvWLI4cOUJrayvBYNDt0AZVsiaySOzJCGNi8Pbbb3PkyBEWLVpEW1sb5eXlKXmxvj8s0RmTYfx+P62trbS1tZGVlcXEiRPxeDz4fD63Qxs0qZjI7aF+Y2IUDAYpLy9n7969rF69mhtuuMHtkAZVKl6js0RnTBx0dnbi9XrZs2fPpzXt0rF4ZzRJzhKdMWnM5/OxY8cOgsEgt912G6NHj07LCXdSMdHZNTpj4uzdd9+lrq6OWbNmMWfOHCorKwkEAm6HFTfJmMgisRadMXHm9Xo5deoUWVlZFBQUUFRUlFaTZMep8GZCWYvOmEGgqlRWVlJUVMSKFSs4fvw4mzdvdjusmCVr1zQSa9EZM0i6CnYeP36cQCDA7NmzGT16tNthxSwVr9FZojNmEDU3N7N582YaGxspKytjwoQ+Z+VLCZbojDE9OnXqFK+++iolJSUsX76ckSNHuh3SgMUr0YlIqYgcF5EaEXmsh/WrReSw89otIteHrasVkXdF5FA0NS3tGp0xCdDU1ERTUxOTJ09mypQp5OXl0dHRQXt7u9uh9Vs8WmzOFAs/JVQUpA7YJyIVqvpe2GZ/AhapapOILCVUv3J+2PrbVbUhmvNZojMmgXbs2EFVVRXLly+nsbGR9evXux1Sv8Sx8OaNQI2qngQQkZcITcXwaaJT1d1h2+8hVN9yQKzrakwCtbS04PF4aGxsJBgMctVVV6Vc8c44dV2jnnbBsRYIH7ZW4A0R2S8iD0c6mSU6YxKsvb2d9evXU11dzcqVK7n66qvdDqlfokx0xV1zwjiv7sko6mkXROR2QonuH8MW36Kqc4GlwLdE5PN9xWxdV2Nc0tDQwLZt28jJyWHx4sXs27cvJaqeRNlia9C+53WNatoFEZkF/AJYqqqNYTGcdd7rReR1Ql3hXb2dzFp0xrjE4/GwZ88esrKymDdvHvn5+WRlJfc0yHF8qH8fMFVEpohINqH5oCvCNxCRy4HXgK+o6vthy3NFJK/rM7AEONLXyaxFZ4zL3nnnHaqrq1m4cCGBQICKigo6OpJ3BoJ4jLqqalBEvg1sBbKAZ1T1qIg84qx/CvgBMAb4mVMcIei0EscBrzvLhgIvqOqWvs5nic4Yl/n9flpaWlLmwf94PcuqqpuATd2WPRX2+evA13vY7yRwffflfbFEZ0wS6OjooKKi4tPPySwZn3yIxBKdMUki2RMcpO5D/ZbojDH9YonOGJP2LNEZY+JORMjLyyMYDNLS0uJ2OElZWDMSu4/OmCSXl5fHV7/6Vb7whS+4HUr6To4jIs+ISL2IHAlb9m8iUu2UT3ldRArD1j3ulF05LiJ3DlLcxmSMYDBIbW0t7e3tzJw50/XinWmZ6IBngdJuy7YBM1V1FvA+8DiAiFxD6A7na519fuaUYzHGDFBLSwsbN27k3LlzfPGLX2Ty5MmuxpOWiU5VdwGfdFv2hqoGna/h5VPKgJdUtV1V/wTUEHoGzRgTo7q6OsrLyxkzZgxLly51bcKdtEx0Ufgafy6fEnXpFRF5uKuyQRxiMCbteTweDh06RHZ2NtOmTSM7O9uVOFIx0cU06ioiTwBB4PmuRT1s1uOfWlXXEaoYiogk39+MMUlq165d7NmzB6/Xm/Bzx7HwZkINONGJyBpgObBY/5zCoyq9YowZuObmZpqbm107fzK22CIZUNdVREoJFcG7R1XDb+ypAFaIyHARmQJMBd6JPUxjTLJIy66riLwI3EaoYmgd8ENCo6zDgW1OqZQ9qvqIU2blFUJ134PAt1Q1+R/gM8ZELRkTWSSSDEHbNTpjEmJ/hKq/EQ0ZMkRzcnIibtfa2hrzueLJHgEzxvRLMjSO+ssSnTGmXzJq1NUYk5msRWeMSWvJOqoaiVUvMcb0S7xuLxGRUqf4R42IPNbDehGR/3bWHxaRudHu250lOmNMv8Qj0TnFPn5KaALqa4CVTlGQcEsJ3Ys7FXgY+Hk/9r2EJTpjTL90dnZGfEXhRqBGVU+qagB4iVBRkHBlwK80ZA9QKCIlUe57iWS5RtcANDvvbivG4ghncVwqleOIR32nrc65I8npVrBjnfN8e5eeCoDM73aM3oqERLPvJZIi0anqZ0SkKhluMLQ4LA6Lo3eq2r025UBFUwCkt22iLh7SJSkSnTEm40RTAKS3bbKj2PcSdo3OGOOGfcBUEZkiItmEKpNXdNumAviqM/q6APCq6rko971EMrXo1kXeJCEsjktZHJeyOOJAVYMi8m1C1/yygGecoiCPOOufAjYBywhVKm8BHupr377OlxQP9RtjzGCyrqsxJu1ZojPGpL2kSHT9fZwjjuedJCI7ROSYiBwVke86y4tEZJuIfOC8D/pEmiKSJSIHRWSjizEUishvnDl7j4nITS7F8bfOz+OIiLwoIjmJiqOXeYx7PfdgzWNs8ynHl+uJbiCPc8RREPh7VZ0BLAC+5Zz7MWC7qk4FtjvfB9t3gWNh392I4Ulgi6peDVzvxJPQOERkAvAoME9VZxK62LwigXE8y1/OY9zjuWVw5zHuKQ6bT3mgonlubTBfwE3A1rDvjwOPuxRLOXAHcBwocZaVAMcH+bwTCf0D+gKw0VmW6BjygT/hDFCFLU90HF13vRcRuitgI7AkkXEAVwBHIv0ddP9dJTQKeNNgxdFt3X3A84mIIx1errfo6MdcsINJRK4A5gB7gXEaul8H533sIJ/+v4B/AMIfEkx0DFcCHwP/63ShfyEiuYmOQ1U/BP4dOA2cI3Tv1BuJjqOb3s7t5u/ugOZTzlTJkOj6/ThH3AMQGQW8CvyNqvoSfO7lQL2q7k/keXswFJgL/FxV5xB69jhh10u7ONe/yoApwHggV0QeTHQcUXLld1dimE85UyVDonN1LlgRGUYoyT2vqq85iz9yqiTgvNcPYgi3APeISC2hKgxfEJFfJzgGCP0c6lR1r/P9N4QSX6Lj+CvgT6r6sapeBF4DbnYhjnC9nTvhv7vy5/mUV6vTT3UjjlSTDImu349zxIuICPBL4Jiq/kfYqgpgjfN5DaFrd4NCVR9X1YmqegWhP/vvVPXBRMbgxHEeOCMi051FiwlNW5nQOAh1WReIyEjn57OY0KBIouMI19u5EzqPsdh8ygPn9kVC5z+lZYRGkU4ATyTwvAsJNfEPA4ec1zJgDKHBgQ+c96IExXMbfx6MSHgMwGygyvn7WA+MdimO/wNUA0eA/0doDuGExAG8SOja4EVCLaW1fZ0beML5vT0OLB3kOGoIXYvr+l19arDjSJeXPQJmjEl7ydB1NcaYQWWJzhiT9izRGWPSniU6Y0zas0RnjEl7luiMMWnPEp0xJu39f5y9A71XmMqsAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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VNBMwpaWljBkz5pvbOUaOHOl2JBPhrJfTBJSq8sUXXzB9+nQ6d+7MQw89RGJiotuxTASyU04TFB6Ph3nz5hEbG8vEiRNJTEwkNjbW7VgmAvmroIlIiojsEJFdIlLvRLAi8msR+VhEtovIW772ab2cEebxxx/n1Vdf5e6776a8vJxx48ZRWVnpdiwTQfzRAhORGGAh3vHeBcAHIrJaVT+rtU1n4AkgRVXzGppbsTZroUWYwsJCtm7dSnl5OR06dGDgwIF2+mn8yk8ttEHALlXNUdUqvFOQpdbZZhTwD1XNc47rcyoyK2gRqKqqinHjxjFnzhyys7Nt3Kfxm1MY+tRNRLbUetWdnToBqD0Vc4GzrrYfAGeIyJsi8qGI3OQrn51yRqjKykry8/N58sknqaqq4vbbb2flypV4PB63o5kw18QWWImP2ajru2my7o5bAz8BhgDtgHdE5F1V3dnQTq2FFsEKCwu59957+frrr5k7dy79+/e3m29Ni/nplLMASKq1nAgU1bPNOlUtV9USYBPwo8Z2agUtCqxcuZIRI0Zw1VVXkZWVxemnn+52JBPG/FTQPgD6ikgvEYnFO+v16jrbrAIuEZHWItIeGMy3H5n5HVbQooDH42HdunW0bduWc845h169etmAdtNs/ihoqloN3Ar8E2+RWq6q20VkoohMdLb5HFgH/Bt4H1iiqtsa269dQ4sSqsptt91Gz549efnll3nzzTeZMGGC27FMmPHnjbOqmg1k11mXUWd5LjC3qfu0FloUKS0tpaioiDfffJPS0lKuv/56myTSnDIb+mRCRklJCRMmTOCjjz7i+eef51e/+pXbkUyYsaFPJuS88847pKWl8YMf/IAFCxbQo0cPtyOZMGEFzYQcj8fzzWPxRowYQVxcnD0iz/hkg9NNSHvwwQe5+uqreeyxx1i0aJE9zNj4ZAXNhKx9+/axa9cucnNzOX78OL/5zW9ITk52O5YJYVbQTEgrKysjLS2NZ599luzsbEaNGuV2JBPCIraXU0Q6i8grIvKFiHwuIj8XkS4iskFEvnTez/BXWBM4NTU15OTk8Ne//pXTTjuNmTNnkpSU5PuLJqpE+jW0+XjHWp2Dd4zV58A9wEZV7QtsdJZNGMjNzeWhhx5CRLjjjjtITk6mTZs2bscyISYiC5qInA78EngKQFWrVPVrvHMaPe1s9jRwdcsimmBbsmQJQ4cOZfLkySxdupR27dq5HcmEkIgsaEBvoBjIEpGtIrJERDoAPVR1D4DzXu8skyIy/uRcSS3IYAIgPz+fd999l+rqarp27cp5551HXFyc27FMiIjUgtYauABYpKoDgXJO4fRSVTNV9UJtfM4k45Lq6mrGjx/PX/7yF15//XX++Mc/uh3JhABt+gSPrmhJQSsAClT1PWf5FbwFbp+IxAE47z6nzTWhqaKigqKiIp577jmOHj3K5MmT7bmfJjJbaKq6F8gXkX7OqiHAZ3jnNBrtrBuNd04jE6b27NnDnXfeyd69e1mwYAE//vGP3Y5kXBbKBa2l0wdNAf7uTNCWA6ThLZLLRSQdyAN+38JjmBDw+uuvU1BQwJAhQ7jqqqu48847OXTokNuxjAvcLFi+tKigqerHQH3XwIa0ZL8m9Hg8HjweDyNGjOCCCy4gKSkJEeHgwYNuRzNBFrEFzUSfu+66i6SkJJ577jnef/99xo0b53YkE0Run1L6YkOfzCk5dOgQ+fn5vP/++5SVlTFy5EjrKIgykdrLaaLUoUOHGDduHG+99RYrVqwgJSXF7UgmiEK5U8AKmmm2rVu3MmnSJBISEpg3b57dfBslrKCZiOTxeMjIyKBjx45cd911xMfH2zCpCBfpg9ON4eGHH2b48OHMmjWLzMxMWre2vqZIFsoFzX7zTIvt3buXw4cPU1xcDMBFF12Ex+MhLy/P5WQmEKyX00S8iooK0tLSWLx4MWvXrmXs2LFuRzIBYr2cJipUV1fj8Xh4+OGHAfjzn/9s03lHGLuGZqJKXl4eDzzwAJWVlcyYMYPevXsTExPjdizjR1bQTNR5/vnnGTZsGKNHj2bZsmV06NDB7UjGT6ygmaiTm5vLpk2baNWqFfHx8fTr14+zzjrL7VjGD0K5oFkvpwmYEydOcMstt9C3b1/WrFnDypUrmTp1qtuxTAucnOAxVFkLzQRUeXk5e/bsYeXKlZSVlZGenk7v3r3djmVaIJRbaFbQTMDt27ePqVOn8tVXX7FkyRJ++tOfuh3JtIAVNGOAjRs38oc//IFBgwaRmZlJ165d3Y5kmiGUC5pdQzNBc3KSyCFDhnDJJZeQmJhIdXU1hw8fdjuaOQWhPFLACpoJuj/96U8kJiayePFiPvvsM9LS0kL6H4n5D7dbYL5YQTNBd+DAAaqrq9m2bRsVFRUMHz6cbdu24fF43I5mmsB6OY2p4/Dhw6Snp5Odnc2qVatITU11O5JpIn9dQxORFBHZISK7RKTBZ/qKyE9F5ISIXONrn1bQjGtUle3bt3PHHXfQpUsX5syZQ3x8vNuxjA/+KGgiEgMsBIYC5wLXi8i5DWz3MPDPpmSzgmZc5fF4mD9/Pm3btmXs2LEkJibStm1bt2OZBvhxcPogYJeq5qhqFfAiUF8zfQqwgiY+sNwKmgkJ8+fPZ9iwYcyYMYPFixcTGxvrdiTTgCYWtG4isqXWa3yd3SQA+bWWC5x13xCRBGAkkNHUbNYpYEJCUVERBw4coLS0lLZt23LBBRdQUFBAQUGB29FMHU1sgZWoan3P7D1J6tt1neXHgLtV9YRIfZt/l7XQTMiorKwkPT2dRx55hHXr1nHLLbe4HcnUw08TPBYASbWWE4GiOttcCLwoIh7gGuAJEbm6sZ22qKCJyO0isl1EtonICyLSVkS6iMgGEfnSeT+jJccw0aWqqoqCggIWLlzI8ePHueuuu+y5nyHEj9fQPgD6ikgvEYkFrgNW1zlWL1Xtqao9gVeASar6amM7bXZBc85vpwIXquoAIMYJdQ+wUVX7AhudZWOarKCggBkzZlBeXs7s2bPp168frVrZyUSo8EdBU9Vq4Fa8vZefA8tVdbuITBSRic3N1tJraK2BdiJyHGiPt8l4L/Br5/OngTeBu1t4HBOFli9fzieffMI111zDqFGjuPXWWzly5IjbsaKev0YKqGo2kF1nXb0dAKo6pin7bPb/9lS1EPhvIA/YAxxW1fVAD1Xd42yzB+he3/dFZPzJHpDmZjCRLTc3l3/961/ExsbSu3dvzj77bM4880y3Y0W9iByc7lwbSwV6AV8DL4vIDU39vqpmApnOvkJ3cJhxVU1NDVOmTOHss8/mlVdeYcOGDdZZ4KJInuDxMmC3qhar6nHgH8BFwD4RiQNw3pt0Q5wxDTly5AiFhYWsX7+e0tJSbrzxRpsk0kWh3EJrSUHLA34mIu3Fe5PIELwX91YDo51tRgOrWhbRGCguLmbSpEl8+umnPPPMM1x88cVuR4paEVnQVPU9vF2pHwGfOvvKBP4GXC4iXwKXO8vG+MXbb7/NTTfdxIABA3jiiSfo3r3eS7QmgCKyoAGo6v2qeo6qDlDVG1W1UlUPqOoQVe3rvB/0V1hjPB4Pzz77LJ06dSIlJYX4+Hg6derkdqyoErEFzRi33H///YwcOZIFCxbw+OOP231qQeLHG2sDwsZymrBUXFzMsWPHyMnJoaqqissuu4ydO3faJJFBEKm9nMa46siRI6SlpfHyyy/z2muvce2117odKSqEcgvNCpoJazU1NezYsYMZM2bQvn17Zs2aRVJSku8vmmazgmZMAOXm5jJ37lxiYmK49dZbSUpKsvnUAiTUr6FZQTMR48knn2To0KFMmzaNp556yma+DZBQLmjWKWAiRkFBAfv376eyspLvfe97nH/++RQWFlJYWOh2tIhinQLGBElVVRU333wzDzzwANnZ2UybNs3tSBHFTjmNCbJjx45RVFREVlYWFRUVTJ061SaJ9CMraMYEWVFREXfddRclJSXMmzePAQMG0NR56U3jrKAZ45LVq1eTmprK0KFDWbp0KZ07d3Y7UtizgmaMSzweD6+//jrt27fnhz/8IcnJyXTt2tXtWGEtlAua9XKaiKeqTJs2jeTkZF588UU2b97MuHHj3I4VllQjd4JHY8LG4cOHKSws5O2336a0tJRrr73WJolsplBuoVlBM1HjwIEDjB8/ns2bN/PSSy8xZMgQtyOFJStoxoSQLVu2MH78eHr27Mn8+fPp0aOH25HCihU0Y0KIx+Nh8eLFdOzYkd/+9rckJCTQoUMHt2OFBbux1pgQNXv2bEaMGMGcOXPIyMggJibG7UhhIZQLmvVymqi1b98+jhw5wp49e6ipqeGSSy4hJyeHvLw8t6OFNOvlNCZEHT16lDFjxpCVlcXatWu56aab3I4U8kK5hWYFzUS9EydOkJOTw6xZs2jdujX3338/3//+992OFZLsGpoxYSAvL48HH3wQVeXuu++mV69etG5tV2TqYwXNmDCRlZVFSkoK48aNIysri/bt27sdKeRYQTMmTOTl5bF582YAunfvTv/+/YmLi3M5VWipqanx+XKLtamNqaO6upoJEybQv39/1qxZw/Lly22iSIfbLTBffLbQRGSpiOwXkW211nURkQ0i8qXzfkatz+4VkV0iskNErghUcGMC6ejRoxQWFvLSSy9x5MgRJk6caGM/HeF+yrkMSKmz7h5go6r2BTY6y4jIucB1wHnOd54QEbtb0YSlvXv3cvvtt5Ofn8+iRYsYOHCg25FCQlgXNFXdBBysszoVeNr5+Wng6lrrX1TVSlXdDewCBvknqjHuWL9+Pddccw2/+MUvWLJkCV26dHE7kqvCuqA1oIeq7gFw3rs76xOA/FrbFTjrvkNExovIFhHZ0swMxgSFx+NhxYoVdOrUicGDB5OUlBTVM9/6q6CJSIpzaWqXiNxTz+f/JSL/dl6bReRHvvbp706B+iZtr/dPp6qZQCaAiITuVUZjHNOnTycxMZFly5bx8ccfM3bsWLcjBZ36aYJH51LUQuByvA2fD0Rktap+Vmuz3cCvVPWQiAzFWy8GN7bf5rbQ9olInBMsDtjvrC8AkmptlwgUNfMYxoSUgwcPkpeXx9atWykrKyM1NTUqnyblpxbaIGCXquaoahXwIt5LVrWPs1lVDzmL7+KtJ41qbkFbDYx2fh4NrKq1/joROU1EegF9gfebeQxjQs7XX39Neno6GzduZOXKlVx55ZVuRwq6Jha0bicvKTmv8XV20+TLU450YK2vbE25beMF4B2gn4gUiEg68DfgchH5Em+T8W/OH3Q7sBz4DFgHTFbVE76OYUy4+eSTT5gyZQrdu3fnkUceIT4+3u1IQdPEglaiqhfWemXW2U2TL0+JyG/wFrS7fWVrSi/n9aoap6ptVDVRVZ9S1QOqOkRV+zrvB2ttP0tVz1bVfqrqs6IaE448Hg8LFy6kffv23HDDDcTHx9OuXTu3YwVcU4pZE085m3R5SkTOB5YAqap6wNdObeiTMS3w6KOPMnz4cGbOnElmZiZt2rRxO1LA+amgfQD0FZFeIhKL9/7V1bU3EJHvA/8AblTVnU3ZqQ19MqYFioqKOHToEAcPHqRNmzYMHjyY3Nxc8vPzfX85TPmjl1NVq0XkVuCfQAywVFW3i8hE5/MM4D6gK94b9AGqVfXCxvYroTAuy27bMOGuTZs2DBo0iHXr1jFv3jzuu+8+tyPV50NfBcGX9u3ba58+fXxu9+mnn7b4WM1hp5zG+MHx48fJy8tj3rx51NTUcM8995CcnOx2LL/z4zW0gLCCZoyf5Ofnc99993Hs2DFmzpxJnz59aNUq8v6JWUEzJoq88MILDBs2jFGjRrFs2TI6duzodiS/soJmTBTJzc3ljTfeoE2bNiQnJ9OnTx+6d+/u+4thwiZ4NCbK1NTUMGnSJPr06cOrr77KmjVrmDJlituxWsztFpgv1kIzJkDKysooKipizZo1lJWVMWbMmIiYJNJOOY2JUvv372fKlCns2LGDrKwsBg9udLKIsGAFzZgot2nTJkaNGsXAgQPJyMigW7dubkdqtlAuaHYNzZggyMnJIScnh1/+8pdceumlJCQkUFVVRWlpqdvRTlkoX0OzkQLGBFG3bt1ISEggIyODnTt3MmbMmGAWiBbfvX/aaadpQkJjs/x47d6920YKGBPpSkpK2L17Nzt37qSiooIrrrgi7CaJDOVTTitoxgRZaWkpY8aM+eZ2jpEjR7od6ZRYQTPGfIuq8sUXXzB9+nQ6d+7MQw89RGKizxmmQ4IVNGPMd3g8HubNm0dsbCwTJ04kMTGR2NhYt2M1yganG2Ma9fjjj5OSksL06dN56qmnOO2009yO1KhQLmh224YxLissLKS4uJjy8nI6dOjAwIEDKSgooKCgwO1o9XJzrKYv1kIzJgRUVVUxbtw45syZQ3Z2dkiP+wzlFpoVNGNCRGVlJfn5+Tz55JMcO3aM22+/PeRu6bBraMaYJissLOTee+/l66+/Zu7cufTv3x9nPv2QYQXNGHNKVq5cyYgRI7jqqqvIysri9NNPdzvSN6ygGWNOicfjYd26dbRt25ZzzjmHXr16hcyAdpvg0RhzylSV2267jZ49e/Lyyy/z5ptvMmHCBNczhcL474b4bKGJyFIR2S8i22qtmysiX4jIv0VkpYh0rvXZvSKyS0R2iMgVAcptTFQoLS2lqKiIN998k9LSUq6//nrXJ4kM91POZUBKnXUbgAGqej6wE7gXQETOxfsE5POc7zwhIjF+S2tMFCopKWHChAl89NFHPP/88/zqV79yNU9YFzRV3QQcrLNuvapWO4vvAicHoaUCL6pqparuBnYBg/yY15io9c4775CWlsYPfvADFixYQI8ePVzJEdYFrQnGAmudnxOA/FqfFTjrvkNExovIFhHZ4ocMxkQ8j8fzzWPxRowYQVxcnCuPyIvYgiYiM4Bq4O8nV9WzWb1/OlXNVNUL1YVJ4IwJZw8++CBXX301jz32GIsWLQrqw4xVNTJ7OUVkNHAlMET/U5ILgKRamyUCRc2PZ4ypa9++fZSXl5Obm8uJEyf4zW9+w65du8jNzQ3K8cO6l7M+IpIC3A1cpapHa320GrhORE4TkV5AX+D9lsc0xtRWVlZGWloazz77LNnZ2YwaNSpoxw7rU04ReQF4B+gnIgUikg48DnQCNojIxyKSAaCq24HlwGfAOmCyqp4IWHpjolhNTQ05OTn89a9/5bTTTmPmzJkkJSX5/mILhXJBs4ekGBMBZs6cyR133MHQoUN57733OH78eH2btfjBJa1atdK2bdv63K6iosKVh6RYQTMmAiQlJZGcnMzkyZOprq5m/PjxVFRU1N3MLwWtKRNQHjt2zJ76ZIxpnvz8fN59912qq6vp2rUr5513HnFxcQE5Vij3cloLzZgI0q5dO84991yys7N57rnnuPPOO2t/7JcWWuvWvm+OOH78uLXQjDEtU1FRQVFREc899xxHjx5l8uTJfp0k0iZ4NMYE1Z49e7jzzjvZu3cvCxYs4Mc//rFf9++vgiYiKc4kFrtE5J56PhcR+R/n83+LyAW+9mkFzZgI9frrrzNy5EguvfRSXn31Vb/t1x8FzZm0YiEwFDgXuN6Z3KK2oXjvZe0LjAcW+dqvFTRjIpTH42HVqlUkJSWRmprqt/36qVNgELBLVXNUtQp4Ee/kFrWlAs+o17tAZxFptKcjVCZ4LAHKnXe3dcNy1GY5vi3scowcOfLkj8l+OO4/nWP70rbOxBOZqppZa7m+iSwG19lHQ5Nd7GnooCFR0FT1TBHZEgoD1S2H5bAcDVPVunMjNldTJrJo8mQXJ9kppzHGDU2ZyOKUJ7uwgmaMccMHQF8R6SUisXhnul5dZ5vVwE1Ob+fPgMOq2uDpJoTIKacj0/cmQWE5vs1yfJvl8ANVrRaRW/Fek4sBlqrqdhGZ6HyeAWQDw/DOfH0USPO135AYKWCMMf5gp5zGmIhhBc0YEzFCoqD5GgIRwOMmicgbIvK5iGwXkduc9V1EZIOIfOm8nxGELDEislVEXnMxQ2cRecV55urnIvJzl3Lc7vz32CYiL4hI22DlaOA5tA0eO1DPobXn4TaP6wWtiUMgAqUauFNV+wM/AyY7x74H2KiqfYGNznKg3QZ8XmvZjQzzgXWqeg7wIydPUHOISAIwFbhQVQfgvWB8XRBzLOO7z6Gt99gBfg5tfTnsebi+NHX0fKBewM+Bf9Zavhe416Usq4DLgR1AnLMuDtgR4OMm4v2HcinwmrMu2BlOB3bjdBTVWh/sHCfvDu+Ctxf+NeD/BDMH0BPY5uvvoO7vKt4eu58HKkedz0YCfw9GjnB6ud5C4xSe5RlIItITGAi8B/RQ534X5717gA//GDAdqD0ILtgZegPFQJZz6rtERDoEO4eqFgL/DeThHeJyWFXXBztHHQ0d283f3WY9DzfShUJBO+XhDX4PINIRWAFMU9XSIB/7SmC/qn4YzOPWozVwAbBIVQfiHVsbtOuZJznXp1KBXkA80EFEbgh2jiZy5XdXWvA83EgXCgXN1Wd5ikgbvMXs76r6D2f1vpOj+p33/QGMcDFwlYh48M44cKmIPBfkDOD971Cgqu85y6/gLXDBznEZsFtVi1X1OPAP4CIXctTW0LGD/rsr/3ke7n+pc37pRo5QFQoFrSlDIAJCRAR4CvhcVR+t9dFqYLTz82i819YCQlXvVdVEVe2J98/+v6p6QzAzODn2Avki0s9ZNQTv4wiDmgPvqebPRKS9899nCN7OiWDnqK2hYwf1ObRiz8P1ze2LeM7/ZIbh7bX5CpgRxOP+Am/T/N/Ax85rGNAV70X6L533LkHK82v+0ykQ9AzAj4Etzt/Hq8AZLuWYCXwBbAOeBU4LVg7gBbzX7o7jbfmkN3ZsYIbze7sDGBrgHLvwXis7+buaEegc4fayoU/GmIgRCqecxhjjF1bQjDERwwqaMSZiWEEzxkQMK2jGmIhhBc0YEzGsoBljIsb/B34JUn58vFD8AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "## Normalization condition\n",
    "for i in range(N):\n",
    "        plt.figure()\n",
    "        plt.imshow(np.round(B[i][0,:,:]@B[i][0,:,:].T.conjugate()+B[i][1,:,:]@B[i][1,:,:].T.conjugate()).real, cmap=plt.cm.gray)\n",
    "        plt.colorbar()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "warming-small",
   "metadata": {},
   "source": [
    "<h1> DALL'INTERNET </h1>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "general-hacker",
   "metadata": {},
   "outputs": [],
   "source": [
    "##### Ex4.1(b): multi-stage decomposition\n",
    "d = 5 # local dimension\n",
    "chi = 3 # max internal dimension \n",
    "H0 = (np.sqrt(1+np.arange(d**7))).reshape(d,d,d,d,d,d,d).transpose(6,5,4,3,2,1,0) \n",
    "\n",
    "# first decomposition\n",
    "utemp,stemp,vhtemp = LA.svd(H0.reshape(d**2,d**5),full_matrices=False)\n",
    "U0 = (utemp[:,:chi]).reshape(d,d,chi)\n",
    "H1 = (np.diag(stemp[:chi]) @ vhtemp[:chi,:]).reshape(chi,d,d,d,d,d)\n",
    "# second decomposition\n",
    "utemp,stemp,vhtemp = LA.svd(H1.transpose(1,2,0,3,4,5).reshape(d**2,chi*d**3),full_matrices=False)\n",
    "U1 = (utemp[:,:chi]).reshape(d,d,chi)\n",
    "H2 = (np.diag(stemp[:chi]) @ vhtemp[:chi,:]).reshape(chi,chi,d,d,d).transpose(1,0,2,3,4)\n",
    "# third decomposition\n",
    "utemp,stemp,vhtemp = LA.svd(H2.reshape(chi**2,d**3),full_matrices=False)\n",
    "U2 = (utemp[:,:chi]).reshape(chi,chi,chi)\n",
    "H3 = (np.diag(stemp[:chi]) @ vhtemp[:chi,:]).reshape(chi,d,d,d)\n",
    "# fourth decomposition\n",
    "utemp,stemp,vhtemp = LA.svd(H3.reshape(chi*d,d**2),full_matrices=False)\n",
    "V3 = vhtemp[:chi,:].reshape(chi,d,d).transpose(1,2,0)\n",
    "H4 = (utemp[:,:chi] @ np.diag(stemp[:chi])).reshape(chi,d,chi)\n",
    "# check result\n",
    "H0recovered = ncon([U0,U1,U2,V3,H4],[[-1,-2,1],[-3,-4,2],[1,2,3],[-6,-7,4],[3,-5,4]])\n",
    "totErr = LA.norm(H0 - H0recovered) / LA.norm(H0)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "supreme-richardson",
   "metadata": {},
   "source": [
    "<h4> References </h4>\n",
    "<blockquote>\n",
    "[1.] Ulrich Schollwöck, <a href=\"https://www.sciencedirect.com/science/article/abs/pii/S0003491610001752?via%3Dihub\">The density-matrix renormalization group in the age of matrix product states</a>\n",
    "</blockquote>"
   ]
  }
 ],
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   "display_name": "Python 3",
   "language": "python",
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  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
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